Windows 10 is most likely an EFI install so the question is, did you also install Mint EFI? You should be able to mount and access the efi partition to see if you have a Mint directory with the boot files, probably will be labelled Ubuntu but I'm not sure. You could post that info here.
Another option would be to boot Mint and go to the site below and download and install boot repair from the ppa per the instructions on the site. After downloading it, run it and select the option to Create BootInfo Summary and post a link to the output here.
What you are describing is generally what happens when one system if EFI and another if the older MBR install.
https://help.ubuntu.com/community/Boot-Repair